ABE425 Engineering Measurement Systems

Strain Gages, Bridges and Load Cells

Dr. Tony E. Grift

Dept. of Agricultural & Biological EngineeringUniversity of Illinois

This presentation covers measuring force (1-3), displacement (4), velocity (5) and acceleration (6)

1. Strain gage (Force)

2. Wheatstone bridge

3. S-type load cell

4. Linear Variable Differential Transformer

6. Accelerometer5. Pro-laser Dopplervelocity sensor

Force measurement

The elongation of a thin wire due to strain changes its electrical resistance which can be measured

Strain and stress in metals are linearly related in the elastic range (Hooke’s law)

Videos (notice ‘necking’)Steel tensile testHDPE tensile test

Elastic range

Strain gages are composed of thin wires that change their resistance by being stretched

The resistance of a thin wire is a function of resistivity, length and cross sectional area

2

*m L mR

A m

Resistance is proportional toResistivity rLength L

And inversely proportional toCross sectional area A

A

L

Manipulate equation to get a resistance change expression

2LR L LA A

A A

*LR

A

R R RR L A

L A

R L A

R L A

Original equation

Change in resistance is a function of partial derivatives

Stick in the partial derivatives

Divide by original resistance equation

Express the change in area in a change in diameter

2

2 2

22

2 24 1

4

D D D D D DA A D

A D DD

A

AD

D

2A D

A D

Use Poisson ratio (material property) to simplify the strain gage equation

2R L D

R L D

2A D

A D

R L A

R L A

Transverse strainAxial strain a t

t a

Poisson ratio

When you stretch a metal it becomes thinner. The negative ratio between transverse and axial strain is the Poisson ratio

L

L+DL

D+DD

D

t a

Transverse strain Axial strain

Poisson ratio

Change in resistance is a function of the Poisson ratio and the change in resistivity (temperature)

2

1 2a t

a

t a

RR

RR

1 2a a

RR

S

Strain gage factor f(temperature)

To measure strain in different directions, strain gages come in rosettes

Rectangular Equiangular

Here is an example of a rectangular strain gage rosette

Strain measurement using Wheatstone bridge

In a quarter bridge circuit the strain gage takes up one branch, there is no temperature compensation

Having four gages in the bridge gives inherent temperature compensation and increased output

+e

-eF

Switching within the bridge is a bad idea since the contact resistances are part of the bridge and the strain gages need to maintain a constant temperature

It is better to switch outside the bridge since 1) there is no current where the contacts are and hence no voltage drops and 2) the temperature of the strain gages is constant

Load cells

Load cells are structures fitted with strain gage sets, and built-in temperature compensation

Cantilever type Hollow cylinder type. When the cylinder is compressed it becomes shorter which is measured by compressive gages and the diameter increases which is measured by the tensile gages

Proving rings are simple devices to calibrate load cells for larger load (up to 250kN)

Dynamometers are power measurement devices based on measuring torque and RPM

Nm radP T Nm Watt

s s

Eddy current dynamometers dissipate energy by generating magnetic fields through eddy currents. The dissipated energy is carried away using a water flow

Nm radP T Nm Watt

s s

Torque can be measured using a shaft torque meter that can be read with a stroboscope

Torque can be measured using angled strain gages and slip rings (watch out for their resistance)

To avoid slip rings, an microcontroller chip can be used with built-in wireless data communication

RFpic 12c509 Dual Inline Package

(DIP)

RFpic 12c509 Surface Mounted Device

(SMD)

Displacement measurement

The slider of a potentiometer can be used as a relatively inaccurate displacement sensor

Rotary potentiometers can be used for inaccurate angle measurement

A Linear Variable Differential Transformer (LVDT) is an accurate sensor for small displacements

LVDT’s are linear in the rated range, outside the range edge effects render them non-linear

In an LVDT the electrical coupling between magnets is provided by a movable core

LVDT’s also come in a rotary version, which allows angle measurements. Notice the complicated core shape

Measuring the phase difference between primary and secondary voltages yields direction

Signal conditioning is used to create a DC signal proportional to displacement with the correct sign for direction

The capacitance of a capacitor is a function of the overlap between its plates. These devices are used to measure extremely small displacements

Non-linear Linear

The change in capacitance can be measured accurately using an AC Wheatstone bridge

Angular encoders can measure a shaft position. They suffer from simultaneous state changes

0000 0 0001 10010 20011 30100 40101 50110 60111 71000 81001 91010 101011 111100 121101 131110 141111 15

Gray code is a much more reliable encoding since no simultaneous state changes occur

0000 0 0001 10011 30010 20110 60111 70101 50100 41100 121101 131111 151110 141010 101011 111001 91000 8

Velocity measurement

The voltage output of a winding is proportional to the velocity of a magnetic core passing it

Winding

Permanent magnet

Voltage is function of speed AND position

The voltage output of a winding is proportional to a magnetic core passing it

Voltage is function of speed NOT position

Doppler shift is the simplest way to measure the speed of an object non-intrusively and linearly

Magnetic pickups (proximity sensors) give pulses from which the shaft RPM can be derived

A stroboscopic tachometer can be used to measure shaft RPM: This method is primitive and obsolete

Contactless tachometers can count the number of times a reflective strip passes per second and give RPM

Accelerometers

Piezoelectric sensors can be used to measure either force or (very small) displacement

A charge amplifier is needed to obtain signals from the Piezoelectric sensor as an accelerometer

Piezoelectric accelerometers have a seismic mass and can measure vibrations up to 25 kHz

Semiconductor type strain gage accelerometers can measure vibrations up to 100 Hz

A servo accelerometer is an accurate automatic compensation method that can measure 50 g

A vibrometer has a relatively large and measures earth quakes vibrations

This is what we covered today. Questions?

1. Strain gage (Force)

2. Wheatstone bridge

3. S-type load cell

4. Linear Variable Differential Transformer

6. Accelerometer5. Pro-laser Dopplervelocity sensor